Micro buses have become much more popular with Nepalis in the past 5 years or so, and there now seem to be lots of them going to many places. I think they have become more popular because they are quicker than the public buses (partly because they stop less often), are less uncomfortable and not that much more expensive.
I was the only foreigner on the micro bus Ktm to BS in Jan 2016 - everyone else was Nepali, only one was to do with trekking (my guide). I think we just turned up on the morning we travelled - but I am not certain. We got the 9.30 bus from Ktm (which then got stuck in traffic on the Ktm ring road...), but from memory the MBs start running at about 6 or 7am to BS (so if we had got an earlier one, we could have got further that first day than Ngadi, but I was being lazy re not getting up early). As the MBs for BS seemed to leave every 30 minutes, I would have thought that you would have a good chance of getting on one if you just turn up.
There are some places that MBs do not go to, usually I think because the roads are too rough. The "other" Nepali I know, whose village is east of Ktm, we could only get there on the local bus, which is slow and uncomfortable. My guides' village, which is north of Ktm (where I have stayed several times) is served by MBs, which have halved the time required compared to the local bus. However the MBs did not go to say Syabrubensi (for Langtang) at that time, as the road was too rough. This will keep changing.
You could get a "tourist" bus to Dumre, arrange to meet your guide there, let him sort out how to get from Dumre to BS, but there is some local "mafia" in Dumre which overcharges tourists using the local (ie public) bus. You should be able to get something from D to BS without too much hassle - I used the MB Ktm to BS as it is much easier, cheaper and quicker than splitting the bus journey at Dumre.